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tensor product graph Cardinal Invariants Subnormal ideal C-sequence Ascent Path Forcing with side conditions Slim tree Kurepa Hypothesis Commutative projection system P-Ideal Dichotomy Nonspecial tree Non-saturation higher Baire space ZFC construction Hedetniemi's conjecture Jonsson cardinal Microscopic Approach Rado's conjecture stationary hitting coloring number Was Ulam right? Club Guessing Singular Density Vanishing levels Reflecting stationary set Universal Sequences Selective Ultrafilter Greatly Mahlo sap OCA positive partition relation Reduced Power very good scale Well-behaved magma Knaster and friends Uniformly homogeneous Successor of Singular Cardinal countably metacompact Prevalent singular cardinals Postprocessing function PFA(S)[S] Ramsey theory over partitions GMA Dushnik-Miller full tree diamond star Partition Relations transformations xbox Whitehead Problem ccc Sigma-Prikry free Boolean algebra Ostaszewski square Closed coloring Shelah's Strong Hypothesis Strongly compact cardinal b-scale Forcing Axioms Luzin set Large Cardinals Poset Small forcing Monotonically far Uniformly coherent Subtle tree property Chang's conjecture Respecting tree Martin's Axiom Interval topology on trees Amenable C-sequence Iterated forcing Prikry-type forcing Hereditarily Lindelöf space Constructible Universe Intersection model Entangled linear order reflection principles Sakurai's Bell inequality Parameterized proxy principle club_AD Successor of Regular Cardinal Foundations specializable Souslin tree Square-Brackets Partition Relations Diamond Partition relations for trees middle diamond Strongly Luzin set O-space Erdos-Hajnal graphs Fast club Sierpinski's onto mapping principle Ineffable cardinal Lipschitz reduction Countryman line Ascending path Axiom R square principles stick Singular cofinality Coherent tree Subtle cardinal Analytic sets polarized partition relation Almost-disjoint family nonmeager set super-Souslin tree Uniformization Local Club Condensation. Knaster Aronszajn tree Cardinal function Rock n' Roll Fat stationary set weak diamond Fodor-type reflection projective Boolean algebra Antichain HOD Rainbow sets Precaliber L-space strongly bounded groups Filter reflection Cohen real weak Kurepa tree Commutative cancellative semigroups Strong coloring unbounded function PFA Ulam matrix Mandelbrot set Generalized descriptive set theory 54G20 AIM forcing Almost countably chromatic Generalized Clubs approachability ideal Chromatic number weak square regressive Souslin tree square Diamond for trees Absoluteness Diamond-sharp Singular cardinals combinatorics S-Space Open Access Distributive tree Forcing Souslin Tree indecomposable filter Almost Souslin Subadditive Minimal Walks free Souslin tree Hindman's Theorem perfectly normal Dowker space incompactness Weakly compact cardinal Erdos Cardinal SNR stationary reflection
Tag Archives: Entangled linear order
Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. We investigate global structural properties of linear orders of a fixed infinite size. It is classical that the countable linear orders and the continuum-sized orders exhibit contrasting behaviours. Modern results show that strong extensions … Continue reading
Posted in Basis problems, Partition Relations, Preprints
Tagged Aronszajn tree, Ascending path, Club Guessing, Countryman line, Entangled linear order, Minimal Walks, Monotonically far, Partition relations for trees, Strong coloring, Subtle tree property, Vanishing levels, ZFC construction
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Strong failures of higher analogs of Hindman’s Theorem
Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring $c:\mathbb R\rightarrow\mathbb Q$, such that … Continue reading
Posted in Groups, Partition Relations, Publications
Tagged 03E02, 03E35, 03E75, 05A17, 05D10, 11P99, 20M14, Chang's conjecture, Commutative cancellative semigroups, Entangled linear order, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
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